Geometry

Question Analysis  

The task is to determine the unit circle coordinates for  by relating it to Quadrant I’s special angles (30°/60°) and adjusting for Quadrant III using reference angles and trigonometric signs.  

 

Key Concept Explanation  

Radians to Reference Angle:  radians (240°) lies in Quadrant III. Its reference angle is  (60°).  

Trig Signs in QIII: Both cosine (x) and sine (y) are negative (ASTC rule: Tan (+), so Sin/Cos (-)).  

 

Step-by-Step Solution  

1. Identify the reference angle:  

Reference angle =  (60°).  

2. Apply Quadrant I ratios for 60°:  

, .  

3. Adjust signs for Quadrant III:  

,